Mrs Clinton’s Puerto Rico win was overwhelming but the turnout was much lower than expected, damaging her hopes of amassing a clear and potentially highly symbolic lead in the overall popular vote.

She nevertheless stated that she was winning the POPULAR vote -a dubious assertion that relies on some creative mathematics.

Just after the Montana polls close, Mr Obama, who could be accompanied by senior Democratic party figures, is to hold a huge rally in St Paul, Minnesota at the venue where John McCain is due to accept the Republican nomination in September.

Mr Obama’s aides were working furiously yesterday to amass the two dozen or so "super-delegates" – party officials whose convention votes are not tied to the primaries – he would need to ensure that the South Dakota and Montana results give him a majority.

Terry McAuliffe, Mrs Clinton's campaign chairman, told ABC News: "We'll see where we are when we finish up Tuesday. Then super-delegates will begin to move. But we're going to make our argument right up until someone has that number."

Howard Dean, the Democratic National Committee chairman, said the nomination would be decided this week: "We don't want to go to the convention, have a big fight at the convention, and lose the presidency."

The Clinton camp was unhappy with the dnc decision, which raised the number of delegates needed for victory from 2,025 to 2,118, but showed little appetite to challenge.

According to the non-aligned RealClearPolitics website, Mr Obama has 2,051 delegates to Mrs Clinton's 1,876.

There were 55 delegates at stake in Puerto Rico, which voted yesterday and 31 will be at stake in South Dakota and Montana.

Mrs Clinton was expected to win in Puerto Rico while Mr Obama appears to have clear leads in the last two states. If the two candidates split the delegates, that would leave Mr Obama needing just 24 of the remaining 178 undecided super-delegates for outright victory.

Even Harold Ickes, Mrs Clinton's fearsomely combative senior adviser, appeared to be close to conceding defeat.

When asked on NBC television whether the former First Lady would congratulate Mr Obama on Tuesday, he responded: "We expect to get the nomination and we're making the case."

Last week, Mrs Clinton said she expected undecided super-delegates to make up their mind quickly after Tuesday.

Her rapidly fading hopes rested on her being able to persuade 90 per cent of them to overturn Mr Obama's delegate lead because of her contention that she would be the stronger candidate against Mr McCain.

Mr Obama indicated on Saturday night that he thought Mrs Clinton, in consultation with her husband Bill, would concede this week so that the party could unite against Mr McCain.

"I think that Senator Clinton and former President Clinton love this country," he said.

"They love the Democratic Party. I think they deeply believe that Democrats need to win in November. And so I trust that they're going to do the right thing."